Explicit expressions of UMVUE for variance components are obtained for a class of models that include balanced cross nested random models. These estimators are used to derive tests for the nullity of variance components. Besides the usual F tests, generalized F tests will be introduced. The separation between both types of tests will be based on a general theorem that holds even for mixed models. It is shown how to estimate the p-value of generalized F tests.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1043,
author = {Miguel Fonseca and Jo\~ao Tiago Mexia and Roman Zmy\'slony},
title = {Estimators and tests for variance components in cross nested orthogonal designs},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {23},
year = {2003},
pages = {175-201},
zbl = {1049.62065},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1043}
}
Miguel Fonseca; João Tiago Mexia; Roman Zmyślony. Estimators and tests for variance components in cross nested orthogonal designs. Discussiones Mathematicae Probability and Statistics, Tome 23 (2003) pp. 175-201. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1043/
[000] [1] M. Fonseca, J.T. Mexia and R. Zmyślony, Estimating and testing of variance components: an application to a grapevine experiment, Biometrical Letters 40 (1) (2003), 1-7.
[001] [2] M. Fonseca, J.T. Mexia and R. Zmyślony, Exact distribution for the generalized F tests, Discuss. Math.-Probability and Satatistics 1,2 (2002), 37-51. | Zbl 1037.62004
[002] [3] A.I. Khuri, Direct Products: A powerful tool for the analysis of balanced data, Commun. Stat. Theory, 11 (1977), 2903-2929. | Zbl 0507.62067
[003] [4] A.I. Khuri, T. Matthew and B.K. Sinha, Statistical Tests for Mixed Linear Models, Wiley 1997.
[004] [5] M. Loeve, Probability Theory, D. van Nostrand Company 1963.
[005] [6] J. Seely and G. Zyskind, Linear spaces and minimum variance unbiased estimation, Ann. Math. Stat. 42 (1971), 691-703. | Zbl 0217.51602
[006] [7] J. Seely and G. Zyskind, Quadratic subspaces and completeness, Ann. Math. Stat. 42 (1971), 710-721. | Zbl 0249.62067
[007] [8] J. Seely, Minimal sufficient statistics and completeness for multivariate normal families, Sankhya, Ser. (A) 39 (1977), 170-185. | Zbl 0409.62004
[008] [9] T.A. Severini, Likelihood Methods in Statistics, Oxford University Press 2000.
[009] [10] W.H. Steeb, Kronecker Product and Applications, Manheim 1991.
[010] [11] R. Zmyślony, Completeness for a family of normal distributions, Mathematical Statistics, Banach Cent. Publ. 6 (1980), 355-357. | Zbl 0464.62003
[011] [12] A. Michalski and R. Zmyślony, Testing hypotheses for variance components in mixed linear models, Statistics (3-4) 27 (1996), 297-310. | Zbl 0842.62059
[012] [13] R. Zmyślony and S. Zontek, On robust estimation of variance components via von Mises functionals, Discuss. Math.-Algebra and Stoch. Methods, 15 (2) (1995), 349-362. | Zbl 0842.62021
[013] [14] A. Michalski and R. Zmyślony, Testing hypotheses for linear functions of parameters in mixed linear models, Tatra Mt. Math. Publ. 17 (1999), 103-110. | Zbl 0987.62012
[014] [15] S. Zontek, Robust estimation in linear models to spatially located sensors and random input, Tatra Mountain Publications 17 (1999), 301-310. | Zbl 1067.62527